Method of designing optical system

ABSTRACT

The design method of the optical system according to the present invention comprises a step (S 1 ) for setting an optical parameter in a design state in which a production error has not been taken into consideration, a step (S 2 ) for making/renewing a production state where an optical parameter in a production state is made by adding the production error to the optical parameter in the design state, or the production error of the optical parameter in an existing production state is renewed, a step (S 3 ) for making an evaluation function which makes the evaluation function and a step (S 4 ) for performing optimization which determines an optimal optical parameter by optimizing the evaluation function.

TECHNICAL FIELD

The present invention relates to a design method of an optical systemthat is especially suitable for performing in a design processingapparatus, such as a computer and the like. It also relates to arecording medium in which a design program of an optical system isrecorded, an optical system and an optical apparatus designed using adesign method of an optical system or a design program of an opticalsystem.

BACKGROUND ART

Conventionally, as a design method of an optical system, the steepestdescent method, the conjugate gradient method, the least-squares method,etc. have been used. Each of these methods is called an optimizationtechnique, and an evaluation function having two or more variables isused.

When these optimization techniques are used for a design of an opticalsystem, what is equivalent to a variable of an evaluation function is anevaluation parameter (or an evaluation criteria), for example, such asaberrations and the like. This evaluation parameter is computed based onthe value of the optical parameter (or composition) of optical systems,such as a radius of curvature of an optical action surface, a surfaceinterval, and a refractive index. Therefore, if a value of the opticalparameter of an optical system is changed, a value of an evaluationparameter changes, and change of the value of an evaluation parameterchanges a value of an evaluation function.

Then, by changing gradually a value of an optical parameter of anoptical system, processing for calculating the optimal value (forexample, the minimum value and the minimal value) of an evaluationfunction is carried out.

Thus, when an optimal value of an evaluation function is obtained, anoptical system having the optimal combination of a value of each opticalparameter of the optical system at that time will be expressed. As aresult, a value of an optical parameter of the optical system nearest toan intention of a designer is obtained. In addition, in case that anoptimal value of an evaluation function is calculated, processing whichan evaluation parameter also brings close to desired targeted valuesimultaneously is carried out.

In this way, in a design of an optical system, an optical parameter ofthe optical system that an evaluation function serves as the optimalvalue, and an evaluation parameter reaches in target tolerance level isdetermined.

For example, in order to reduce change of performance of an opticalsystem by a production error adding some correction to a design value,and applying a limitation to the number of variables for optimization,etc. have been made. Such correction and limitation are carried out by adesigner's own handwork. This handwork is carried out based on know-howand the like such as a design value obtained by computer, knowledge andexperience of thea designer.

However, in recent years new design methods of an optical system havebeen proposed by, for example, Japanese published unexamined patentapplication Toku Kai Hei 11-30746, Japanese published unexamined patentapplication Toku Kai Hei 11-223764, Japanese published unexamined patentapplication Toku Kai Hei 11-223769, Patent No. 3006611, Japanesepublished unexamined patent application Toku Kai 2002-267926,etc.

DISCLOSURE OF THE INVENTION

In order to attain the purpose mentioned above, a design method of anoptical system according to the present invention, in the design methodof an optical system using an evaluation function, comprises a step forsetting an initial value which sets up an optical parameter in a designstate where a production error has not been taken into consideration, astep for making the evaluation function which makes the evaluationfunction, and a step for performing optimization which determines anoptimal optical parameter by optimizing the evaluation function.

The design method of the optical system of the present invention isconstituted such that in the step for making for the productionstate•renewing,

a quantity of the production error to be applied is acquired, based on avalue in a table of an amount of error which has been establishedbeforehand according to a requirement for acquisition of an amount of aproduction error, the amount of the error is applied to an opticalparameter in the design state, and thus an optical parameter in theproduction state is newly made, or a value of the amount of error whichhas been applied to the optical parameter in the existing productionstate is renewed according to change of the optical parameter in thedesign state.

In the design method of the optical system of the present invention, inthe step for making an evaluation function, at least one productionerror sensitivity parameter determined based on the optical performanceof the design state and a production state is included as an evaluationparameter, in addition to the evaluation parameter of the evaluationfunction.

According to the design method of the optical system of the presentinvention, it is suitable for use of computer, wherein various kinds ofaberrations etc. can be corrected and change of performance of theoptical system owing to a production error is hard to occur. Thus, anoptical system can be designed efficiently. Therefore, a design of anoptical system can be efficiently carried out.

Other purposes, features, and advantages of the present invention thanthese mentioned above will become clear by the following detailedexplanation with reference to accompanying drawings.

BRIEF EXPLANATION OF THE DRAWINGS

FIG. 1 is a flow chart showing whole design procedure of a firstembodiment of a design method of an optical system according to thepresent invention.

FIG. 2 is a flow chart showing a concrete processing procedure of anoptimization implementation step of a second embodiment of a designmethod of an optical system according to the present invention.

FIG. 3 is a flow chart showing a concrete processing procedure of a stepfor making/renewing of production state of a third embodiment of adesign method of an optical system according to the present invention.

FIG. 4 is a flow chart showing a concrete processing procedure of amaking/renewing of production error of the fourth embodiment of a designmethod of an optical system according to the present invention.

FIG. 5 is a block diagram showing a constitution of a processingapparatus for implementing a design method of the optical system of thepresent invention.

BEST MODE FOR CARRYING OUT THE INVENTION

Prior to explaining embodiments of the present invention, two differentstates used in an optical design of the present invention will beexplained.

In a stage of a preliminary design of an optical system, as for opticalparameters, such as a radius of curvature of an optical action surfacewhich constitutes an optical system, a lens thickness and an air spaceinterval, generally, only a case where an actual optical system couldhave been made completely without any error is assumed. In the presentinvention, a state of an ideal optical system without any error iscalled a design state. This design state is a state where the opticalsystem consists of predetermined optical parameters. Such predeterminedoptical parameters are optical parameters obtained by such premise thatany production error does not generate.

On the other hand, in an actual optical system, a value of an opticalparameter which constitutes the optical system becomes a different valuefrom that in a design state by a production error. Therefore, there is acase that a performance of an optical system differs from a performancein the design state. Thus, in the design stage, it is necessary to takeinto consideration of a performance different from that in the designstage. Therefore, a production error is given to at least one opticalparameter among optical parameters in the design state. Thus, a state inwhich a composition of the optical system has been slightly changed fromthe design state is set up. In the present invention, this state iscalled a production state.

In the production state, it is desirable that for all actual productionerrors can be reproduced. That is, it is ideal that all errors are givento optical parameters in the design state. However, it is unrealisticthat all errors having distribution are given (reproduced)comprehensively. Then, a central value based on actual productioncapacity as an amount of error δ given to an optical parameter is used.As for an errors to be given to a specific optical parameter A, twokinds of errors, A+δ and A−δ can be considered.

Therefore, the amount of error to be given is good enough at either A+δor A−δ. As a matter of course, if both of A+δ and A−δ are given, it goeswithout saying that the influence of an error can be more exactly takeninto consideration.

Further, as for making of a production state the following two cases canbe considered. One is a case where one kind of production errors isgiven to one optical parameter, and one production state is made. Suchexample will be shown below. Here, a, b, c and d are production errors,a kind of which differs, respectively.

-   a production state A=an optical parameter in a design state A+ a    production error a-   a production state B=an optical parameter in a design state B+    production error b-   a production state C=an optical parameter in a design state C+ a    production error c-   a production state D=an optical parameter in a design state D+ a    production error d.

For example, when an optical parameter A is a radius of curvature, aproduction error a is Newton number (lines). Further, when opticalparameter B is a thickness of a lens, a production error b is athickness error. In this case, an evaluation function F becomes anevaluation function F (production state A, production state B,production state C, production state D). In this case, since change ofan optical performance by each error can be grasped, it is suitable forelucidation of a phenomenon.

Another is a case that two or more kinds of production errors are givento one optical parameter, and one production state is made. Such examplewill be shown below. Here, a, b, c, and d are production errors, a kindof which differs, respectively.

a production state X=an optical parameter in a design state A+ aproduction error a+ production error a′+ an optical parameter B+ aproduction error b

a production state Y=an optical parameter in a design state C+ aproduction error c+ an optical parameter in a design state D+ aproduction error d

For example, when an optical parameter A is a radius of curvature, aproduction error a is Newton number and a production error a′ isastigmatism. Further, when optical parameter B is a thickness of a lens,a production error b is a thickness error.

In this case, an evaluation function F becomes an evaluation function F(a production state X, a production state Y). In this case, change of anoptical performance generated by overlapping an error in two or moreoptical parameters can be grasped. As mentioned above, total number ofproduction states can be suppressed at few number, compared with a casewhere a production state is made for every kind of each of productionerrors. A method which is used for creating a production state isdetermined by a specification of the optical system to be designed, adegree of the influence by an error, etc. Namely, a designer can justchoose one of methods by own judgment. Otherwise, an optical design canalso be carried out by making an evaluation function of both and usingthe evaluation function combined, for example, as an evaluation functionF (a production state A, a production state X) etc.

Next, embodiments of the present invention will be explained for everystep.

FIG. 1 is a flow chart of a design method showing one of embodiments ofthe design method of an optical system. The design method of the opticalsystem of the present invention comprises a step for setting an initialvalue (Step S1), a step for making of production state/renewing, a stepfor making of an evaluation function (Step S3), a step for performing ofan optimization (Step S4) and a step of an effect judging (Step S5).

First, the step for setting an initial value (Step S1) will beexplained. In a step for setting an initial value, a designer sets up avalue of an optical parameter in a design state. As this value of theoptical parameter, a value of an optical parameter of the optical systemdesigned in the past can be used. Otherwise, the value of an opticalparameter can be set up, based on data of a new optical system obtainedby carrying out an optical design.

Next, a step for making/renewing of production state (Step S2) will beexplained. At this step, an amount of error to be given to the value ofthe optical parameter in the design state is determined. Here, a pointof features is that this amount of error is not a value such that adesigner may determine arbitrarily, but a value determined, based on aproduction capacity of the optical system.

In the present embodiment, in order to obtain this amount of error to begiven, a table of an amount of error is prepared beforehand. This tableof an amount of error is made based on requirements for acquisition ofproduction error. Moreover, a value of the data of this table of anamount of error is determined by taking into consideration of aproduction capacity etc.

In the present invention, requirements for acquisition of productionerror means the following three.

(1) Kinds of Production Errors which Should be Given:

For example, Newton error (Newton number), astigmatism, a wall thicknesserror, a lens interval error, a shift eccentricity, a tilt eccentricity,etc.

(2) Kinds of Optical Parameters in a Design State:

For example, a radius of curvature of an optical action surface or alens surface, a lens thickness, a lens interval, an outer diameter, etc.

(3) Conditions by the Value of Optical Parameters:

For example, a range of the value of the optical parameter where theamount of errors to be given can become the same value is divided bycondition.

However, there is a case that numerical conditions of the opticalparameter does not exist, where an amount of error cannot be determinedby only condition (1) or (2)

For example, a table of an amount of error of a radius of curvature isshown in Table 1. Here, the kinds of production error are Newton errorand astigmatism. An optical parameter is a radius of curvature.Moreover, conditions of numerical values of the optical parameter isdivided into five, and ranges of the value of the optical parameter usedas each of conditions are shown in the following table 1. TABLE 1 radiusof curvature of a design state r |10| ≦ |100| ≦ |500| ≦ r < r < r < r <|10| |100| |500| |1000| |1000| ≦ r Newton(lines) 7 7 10 15 20astigmatism 5 6 8 10 15 (lines) . . . . . . . . . . . . . . . . . .

In Table 1, the radius of curvature of a design state is divided by fivenumerical value ranges. The number of Newton and the number ofastigmatism are set up about each of the numerical value ranges. In thedesign method of the optical system of the present invention, a designis carried out with reference to this table of an amount of error. Thatis, a amount of error to be given to a value of the optical parameter ofa design state is acquired from this table of an amount of error. Then,the acquired amount of error is given to the value of the opticalparameter of the design state, and a value of the optical parameter in aproduction state is newly made. In this case, a step for making/renewingof production state becomes a step for making a production state.

Otherwise, it can also change into a new amount of error in the courseof designing of an optical system. If an optical system is furtherdesigned in the first production state, the value of the opticalparameter will change. For example, it is assumed that a value of aradius of curvature (optical parameter) that has been 90 in the firstproduction state changes to 120. In this case, a amount of error ofNewton number (production error) is renewed from seven to ten, based onthe error table of Table 1.

Thus, based on the table of an amount of error, the amount of errorgiven to the value of the optical parameter in the existing productionstate is renewed or changed. In this case, a step of making/renewing ofproduction state becomes a step which renews a production state.

Values of a table of an amount of error have been determined based on anactual production capacity. Therefore, if design is carried out usingsuch table of an amount of error, it will become easy to obtain anoptical system corresponding to the actual production capacity. This isdesirable, since an amount of error is automatically determined based onthe table of an amount of error, and a design can be efficiently carriedout.

Furthermore, more than one kind of table of an amount of error can beused. It is good to make many kinds of table of an amount of errors formaking a synoptic table. Thus, by this way, a designer can give anamount of error while referring to the synoptic table. It is good toconstitute as an error database (hereinafter it is abbreviated by ErrorDB) by recording on a computer. In this way, it will become unnecessaryfor a designer to consider a suitable amount of error each time. Thus, adesign of an optical system can be efficiently made.

Furthermore, it is desirable that programming of the step ofmaking/renewing of production state of the present embodiment is made.In this way, it will become a step available in an optical designsoftware (hereinafter, it is abbreviated by Optical CAD). Optical CAD isone of design tools available on a computer. Therefore, the stepmentioned above is incorporable into Optical CAD. In this way, an amountof error is acquired from Error DB, and by using this amount of error; aproduction state can be newly made on an optical design tool. Or, anexisting production state can be renewed. As a result, it is possible toprocess automatically from acquisition of an error to making andrenewing of a production state. Thus, a design of an optical system canbe efficiently made further.

As a making method of a production state, there is a method in which anproduction error is given to two and more optical parameters, and oneproduction state is made. In this case, as for a step of making/renewingof production state of the present embodiment, it is desirable to carryout it as follows.

First, a designer chooses at least one kind of evaluation parameters towhich the designer-self pays attention. And the kind of production errorgiven to an optical parameter is chosen. Then, an amount of error isgiven to a value of the optical parameter of a design state based on atable of an amount of error.

In that case, an amount of error is chosen from the table of an amountof error so that a value of this selected evaluation parameter maybecome the worst.

It is because a value of plus and a value of minus (+δ, −δ) as an amountof error to be given can be chosen. Therefore, there is a possibilitythat some combination may eliminate an influence of a production erroras a whole. That is, although an amount of error is given, it will be ina production state that there is no influence of the production error.Then, it is made for a value of an evaluation parameter to become theworst. In this way, a case in which an influence of a production erroris overlooked by canceling an influence with a production error owing tosome combination of an amount of error to be given can be eliminated.

Furthermore, as for the making of production state and renewing stare ofthis enforcement form, it is desirable preferably to constitute theamount of error given to the value of an optical parameter so that itmay set up automatically. In this case, it is good to combine Optics CADand Error DB.

When a basic design by Optics CAD is completed, a design state isobtained. At this time, a value of the optical parameter of a designstate is stored in a memory of a computer. Therefore, if the value ofthe memory is referred to, an amount of error can be acquired from ErrorDB. In this way, an amount of error given to the value of an opticalparameter can be automatically chosen from the table of an amount oferror. Thus, a design of an optical system can be efficiently madefurther since it becomes possible to carry out automatically fromacquisition of an error to a making/renewing of a production state. Whenan amount of error is given, based on a table of an amount of error,processing for checking that a value of a desired evaluation parametermay become the worst is set to be carried out simultaneously.

Next, an evaluation function making step (Step S3) and an optimizationimplementation step (Step S4) will be explained altogether. First, anevaluation function is explained. Generally, in a design method of anoptical system using an evaluation function, the evaluation functionconsists of, at least, one evaluation parameter. Each of evaluationparameters consists of an amount of evaluation, a weight, etc., such asan optical performance and the like. As an amount of evaluation of theoptical performance, there is such a thing that is an aberrationdetermined by the optical parameter. As for the weight, a designerdetermines the weight of an amount of evaluation in the whole evaluationfunction.

For example, when an evaluation function is set to F, an evaluationparameter is set to Pi, a desired value of an evaluation parameter isset to Qi, and an assigned weight of an evaluation parameter is set toWi, the evaluation function F can be expressed as follows:F=ΣWi(Pi−Qi)²

As an evaluation parameter here, specification, performance, and thelike of an optical system expressing an optical performance, such asvarious aberrations and a focal length of the optical system, can beused. In an optical design, such evaluation function is made. Then,optimization is carried out to this evaluation function. By thisoptimization, a combination of the optimal optical parameter can bedetermined. A design of an optical system is implemented by carrying outsuch processing. Here, the purpose of optimization is to obtain a valueof an optical parameter which is closer as much as possible to a targetperformance and specification by using a given evaluation function. Asfor a method of optimization, various kinds of methods, such as methodof least squares, etc. mentioned above have been known. However, as formethod of optimization used in the design method of the optical systemof the present invention, any of known methods can be used. Here, anexplanation of concrete contents of the method of optimization isomitted, since it is not directly related to the present invention.

In the design method of the optical system of the present invention Inaddition to evaluation parameters such as an optical performance in adesign state, etc. that have been used so far, new evaluation parameteris introduced. This new evaluation parameter is a production errorsensitivity parameter. This production error sensitivity parameterconsists of an optical performance of a production state, etc. In thepresent embodiment, this production error sensitivity parameter isintroduced so as to carry out optimization.

The production error sensitivity parameter X in the present embodimentis an evaluation parameter which consists of an optical performance y₀in a design state, and an optical performance y_(i) in a productionstate. This is a quantity that can be generally expressed as follows byusing an arbitrary function F.X=F(y ₀ , y _(i))

As an example, a method for obtaining a production error sensitivityparameter from states which are a design state No, and production statesN₁ and N₂ will be explained. Here, a method how to obtain based onquality engineering will be explained. As to a design state No, opticalperformances y₀₁, y₀₂ - - - , y_(0k) in conditions of 1, 2, - - - , k,are determined. Next, also as to production states N₁ and N₂, opticalperformances y₁₁ and y₁₂, - - - , y_(1k), y₂₁ and y₂₂, - - - , y_(2k)are determined similarly. This list is shown in Table 2. TABLE 2 1 2 . .. k N₀ y₀₁ y₀₂ . . . y_(0k) N₁ y₁₁ y₁₂ . . . y_(1k) N₂ y₂₁ y₂₂ . . .y_(2k)

As an optical performance here, there are aberration, spot RMS and MTF,a light intensity, etc. As a condition, FNO, NA, object distance, animage height, etc. are mentioned.

Now, after making such data table, the following various kinds ofparameter are calculated. As to meanings of the parameters, since theyhave been explained in literatures of general quality engineering infull detail, such explanation is omitted here.L1=Σy ₀ _(j) y _(1j) =y ₀₁ y ₁₁ +y ₀₂ y ₁₂ + . . . +y _(0k) y _(1k)L2=Σy _(0j) y _(2j) =y ₀₁ y ₂₁ +y ₀₂ y ₂₂ + . . . +y _(0k) y _(2k)r=y _(0j) ² =y ₀₁ ² +y ₀₂ ² + . . . +y _(0k) ²S _(T) =Σ Σ y _(ij) ² =y ₁₁ ² +y ₁₂ ² + . . . +y _(1k) ² +y ₂₁ ² +y ₂₂² + . . . +y _(2k) ²S _(β)=(L1+L2)²/2rS _(N×β=() L1² +L2²)/r−S _(β)S _(e) =S _(T) −S _(β) −S _(N×β)f _(e)=2k−2f _(N)=2k−1V _(e) =S _(e) /f _(e)V _(N)=(S _(N×β) +S _(e))/f _(N)X=10 log}(S _(β) −V _(e))/V _(N)}

From the parameters mentioned above, a production error sensitivityparameter X can be calculated as follows.X=10 log}(S _(β) −V _(e))/V _(N)}

This production error sensitivity parameter expresses a stability of aproduction error, and has a characteristic in which a value becomeslarge to an extent that it is hard to be influenced by production. Thus,when the production error sensitivity parameter is used, a level of theinfluence of the production error can be easily grasped, and accordinglya design can be efficiently carried out. Here, the production errorsensitivity parameter shows a level of the influence of the productionerror from a design state and a production state.

Now, an evaluation function incorporating a production error sensitivityparameter is set to F′. Then, by including the evaluation function Fexplained previously, an evaluation function F′ is newly made asfollows:F′=F+Σ wj(Xj−Yj)wherein Xj is a production error sensitivity parameter, Yj is a desiredvalue of the production error sensitivity parameter. wj is a weightassigned to the production error sensitivity parameter.

When such evaluation function F′ is made, in a state including theinfluence of a production error, optimization of an optical system canbe carried out. As a result, an optical parameter which cannot be easilyinfluenced of a production error can be obtained efficiently.

Furthermore, an evaluation function is incorporate in a program so thatit can be processed on a computer. Then, each step is constituted sothat optimization may be carried out by the computer. In this way, anoptical system can be designed more efficiently.

Finally, in a step for judging effect (Step S5), whether the desiredspecification, the desired engine performance, etc. are satisfied in theoptical system obtained by the optimization is judged. Here, the designwill be ended if the optical system has such desired specification andperformance. On the other hand, when that is not the case, it returns tothe step for making/renewing of production state, or a step for settingan initial value. Then, the design processing of an optical system isrepeated.

Next, embodiments of the present invention will be explained usingdrawings.

First Embodiment

FIG. 1 shows a first embodiment of a design method of an optical system.Here, a flow chart showing whole design procedure is shown.

In the design method of the optical system of this embodiment, firstly,in a step for setting an initial value (Step S1), a value of an opticalparameter in a design state is set up. A production error is not takeninto consideration in this design state.

Next, in the step of a making/renewing of production state an amount oferror of the production error is given to the value of the opticalparameter of the design state. Or, instead of the amount of error towhich the value of the optical parameter in a production state has beengiven, a new amount of error is given. In this case, it becomes renewingof an amount of error. By this, the value of an optical parameter in theproduction state is set up (Step S2). This amount of error is determinedautomatically by referring to Error DB.

Next, in an evaluation function making step, a kind of evaluationparameter of an evaluation function is determined so that a desiredspecification and performance may be satisfied. In this case, thedesired value and assigned weight are given. By such way, an evaluationfunction is determined (Step S3).

Next, in a step for performing optimization, the optimization is carriedout based on a predetermined evaluation function. Then, an optimaloptical parameter for an evaluation function is determined (Step S4).Here, the evaluation function is made in the step for making theevaluation function ( not illustrated).

Next, in a step for judging effect, From the optical parameter obtainedby the a step for performing optimization, it is judged whether thespecification and the performance of the optical system are the desiredspecification and performance (Step S5). In the effect judging step,when the optical parameter used as the desired specification andperformance has been obtained, the design of the optical system isterminated. On the other hand, when the desired specification andperformance have not been obtained, it returns to the step ofmaking/renewing of production state, while keeping with the presentoptical parameter. If it returns to the step of making/renewing ofproduction state, the amount of error of the optical parameter in theproduction state will be renewed. Then, design processing continues by arenewed amount of error. When it is necessary that a certain change isgiven to a value of the optical parameter of a design state, it returnsto the step for setting an initial value.

According to the design procedure of the optical system of the firstembodiment, an optical design can be carried out efficiently, taking aproduction error into consideration. As a result, an optical system withlittle influence of a production error can be obtained easily. Moreover,yield rate can be improved and production cost can be held down.

Second Embodiment

FIG. 2 shows a second embodiment of a design method of an opticalsystem. Here, a concrete procedure of a step for performing optimizationis shown by a flow chart.

In the step for performing optimization of this embodiment, firstly thevalue E0 of an evaluation function is calculated and memorized, based onthe value of the optical parameter set up (Step S11). Then, theoptimization is performed, based on the evaluation function, and thevalue of an optical parameter is changed and set up (Step S12). Next, avalue E1 of the evaluation function is calculated and memorized, basedon the value of the optical parameter after change (Step S13).

Next, from values E0 and E1 of the evaluation function memorized, animprovement factor ΔE=−E1−E01 of the evaluation function is calculated(Step S14). Here, ΔE is an index for judging how much the evaluationfunction has been improved from a state in which optimization has notyet been performed. This index ΔE shows whether it approaches to anoptimal optical system for the evaluation function or not. At Step S14,it is judged whether the improvement factor is larger than a standardvalue Ec for judgment set up beforehand.

In case that the improvement factor index ΔE is smaller than thestandard value Ec for judgment set up beforehand, namely, it is assumedthat it is Δ E<Ec. In this case, even if optimization is carried outfurthermore it is judged that it does not lead to a remarkableimprovement of the evaluation function, and accordingly optimization isterminated.

On the other hand, in case that the improvement factor index ΔE issmaller, than the standard value for judgment Ec set up beforehand, thatis, it is assumed that it is ΔE≧Ec. In this case, a production state isrenewed (Step S15). Then, it returns to step S11 and the same processingas henceforth is repeated. After the step S14, only the renewing portionof a production state is used.

According to the procedure for performing optimization of the secondembodiment, an amount of error suitable for the optical parameter whichchanges in an optimizing stage can be given.

Third Embodiment

FIG. 3 shows a third embodiment of a design method of an optical system.Here, a concrete procedure of performing a step for making/renewing ofproduction state is shown in a flow chart.

In the step for making/renewing of a production state in the presentembodiment, firstly, whether the production state exists or not isjudged (Step S21). When the production state is not made, processingafter Step S28 mentioned later is carried out.

On the other hand, when the production state has been already made,renewing of the production state is carried out. Then, processing ofStep S22-Step S27 is repeated by only the number of production states.Processing of Step S23-Step S26 is repeated by only the number of theproduction errors given to one production state. That is, in the stepS22 the maximum number of the production state is stored in parameterImax. Then, a production state that is an object of renewing isspecified. Production state number i represents a production state thatis the object of renewing, out of production states, the number of whichis Imax.

In step S23, the maximum number of production error is stored inparameter Jmax. A production error at this time represents a productionerror given to a production state that is the object of renewing. Then,the production error that is the object of renewing is specified.Production error number j represents a production error that is theobject of renewing out of the production errors, the number of which isJmax

This production error number j has the following information. Itrepresents a kind of production error, a kind of optical parameter towhich the production error is given, and a part where the productionerror is given in the optical parameter. For example, the followingTable 3 shows that a production error number 1 means that the productionerror is Newton error, which is given to a radius of curvature and afirst surface of an optical system. TABLE 3 Kind of Production errorproduction Optical number: j error parameter Portion applied 1 NewtonRadius of First surface number curvature (lines) 2 Astigmatism Radius ofSecond surface curvature . . . . . . . . . — J max Thickness CenterThird lens error portion thickness

In step 24, a requirement for acquisition of production error isobtained and stored. This point will be explained. As mentioned above,the production error number j has the kind of production error, the kindof optical parameter, and the information about a portion applied.Therefore, from the information on the applied portion, a value of theoptical parameter in the applied portion (for example, a value of theradius of curvature r of the first surface) can be known. That is, fromthe information on production error number j, requirements for obtainingproduction error which constitute an error table can be obtained.

In step S25, the table of an amount of error is referred to, based onthe requirement for acquisition of production error obtained at the step24, An amount of error obtained by referring is given as a new amount oferror. That is, an amount of error is renewed.

In step S26, what added 1 to the present error number j, is consideredas a new error number. Then, it is judged whether the new error number jexceeds the number of error Jmax or not. When the new the number oferror j exceeds the number of error Jmax, Step S27 is processed. On theother hand, when not exceeding, processing from the Step S23 isrepeated. In step S27, what added 1 to the present error number i isconsidered as a new error number. Then, it is judged whether the newerror number i exceeds the number of error Imax or not. When the new thenumber of error i exceeds the number of error Imax, Step S28 isprocessed. On the other hand, when not exceeding, processing from theStep S22 is repeated.

Next, in step S28, it is judged whether a production state is to be madenewly or not. When the production state is not made, a process formaking/renewing of production state is terminated. On the other hand,when the production state is made, processing after the Step S28 iscarried out.

In step S29, a model of the production state is made. Here, the model ofthe production state is a copy of a design state. That is, a value ofoptical parameter of the model in the design state is the same to avalue of optical parameter of the design state. The production error isthat a production error is added to a design state. Therefore, if thedesign state is one, the design state will be lost by adding aproduction error. Then, things having the same state as a design state,that is, many models are made. If such processing mentioned above iscarried out, one design state can always remain.

Next, the kind and place of an error to be added are set up, and arequirement for acquisition of production error is obtained and stored(Step S30). Table 3 illustrated above is used for setting the kind andthe place of the error to be added. Next, an amount of error is obtainedwith reference to the table of an amount of error from the acquiredrequirement for production error acquisition. Then, the amount of erroris applied to the optical parameter in the model of the design state,and this is regarded as the present production state (Step S31)

Next, in an optical parameter in the present production state, it isjudged whether other errors are to be added newly or not (Step S32).

When other errors are not added, processing from the following step S33is carried out. On the other hand, when other errors are added, itreturns to Step S30 and processing after the step is carried out again.In the step S33, furthermore, a new production state is made, that is,it is judged whether another production state is newly made or not.

When new production state is not made, a process for making/renewing ofproduction state is terminated. On the other hand, when the productionstate is made, it returns to Step S29 and processing after the step iscarried out again.

According to the process procedure of the making/renewing of productionstate in the third embodiment, renewing of an existing production stateand giving of new production state can be simultaneously carried outefficiently. Therefore, a design can be efficiently carried out.

Fourth Embodiment

FIG. 4 shows a fourth embodiment of a design method of an opticalsystem. Here, a concrete processing procedure of a step formaking/renewing of production error is shown in a flow chart. The stepfor making/renewing of a production error of this embodiment is almostthe same processing procedure in the third embodiment. However, in steadof step S25 in the third embodiment, a step (step S25′) using an errorDB recording the table of an amount of error is used.

In step S25′, a requirement for obtaining a production error of a designstate is inputted into a database from the kind and place of the errorgiven. By this way, the amount of error which should be given isobtained from the data base, and a value of the present error isrenewed.

According to the processing procedure for making/renewing of aproduction error of the fourth embodiment, reference of a table of anamount of error can be efficiently carried out using a computer.Therefore, giving newly a production state and renewing of the existingproduction state can be simultaneously carried out much moreefficiently. Thus, a higher efficiency of design of an optical systemcan be obtained further.

Fifth Embodiment

A fifth embodiment of a design method of an optical system is shown.Here, an example in the case of determining for a production errorsensitivity parameter is shown. In this embodiment, an example forobtaining a production error sensitivity parameter when a design stateN₀, a production state N₁ and N₂ exist will be explained.

First, as to a design state N₀, optical performances y₀₁, y₀₂ - - - ,y_(0k) in conditions of 1, 2, - - - , k, are determined. Next, also asto production states N₁ and N₂, optical performances y₁₁ and y₁₂, - - -, y_(1k), y₂₁ and y₂₂, - - - , y_(2k) are determined similarly to thedesign state N₀.

This list is shown in Table 4. TABLE 4 1 2 . . . k N₀ y₀₁ y₀₂ . . .y_(0k) N₁ y₁₁ y₁₂ . . . y_(1k) N₂ y₂₁ y₂₂ . . . y_(2k)

As an optical performance here, there are aberration, spot RMS, MTF,light intensity, etc. As a condition factor, there are FNO, NA, anobject distance, an image height, etc.

Now, after such data table has been made, the following parameters arecalculated.L1=Σ y ₀ _(j) y _(1j) =y ₀₁ y ₁₁ +y ₀₂ y ₂ + . . . +y _(0k) y _(1k)L2=Σ y _(0j) y _(2j) =y ₀₁ y ₂₁ +y ₀₂ y ₂₂ + . . . +y _(0k) y _(2k)r=Σ y _(0j) ² =y ₀₁ ² +y ₀₂ ² + . . . +y _(0k) ²S _(T) =Σ Σ y _(ij) ² =y ₁₁ ² +y ₁₂ ² + . . . +y _(1k) ² +y ₂₁ ² +y ₂₂² + . . . +y _(2k) ²S _(β)=(L1+L2)²/2rS _(N×β)=(L1² +L2²)/r−S _(β)S _(e) =S _(T) −S _(β) −S _(N×β)f _(e)=2k−2f _(N)=2k−1V _(e) =S _(e) /f _(e)V _(N)=(S _(N×β) +S _(e))/f _(N)

From the parameters mentioned above, a production error sensitivityparameter X is calculated as follows.X=10 log{(S _(β) −V _(e))/V _(N)}

Sixth Embodiment

A sixth embodiment of a design method of an optical system is shown.

Here also, another example in the case of determining for a productionerror sensitivity parameter is shown. In this embodiment, there are astate of a design state N₀, and production states N₁ and N₂.Furthermore, an error given to production states N₁ and N₂ has becomeA+δ to N₁, and A−δ to N₂. An example, in such case for obtaining aproduction error sensitivity parameter is shown.

First, as to a design state N₀, optical performances y₀₁, y₀₂ - - - ,y_(0k) in conditions of 1, 2, - - - , k, are determined. Next, also asto production states N₁ and N₂, optical performances y′₁₁ andy′₁₂, - - - , y′_(1k), y′₂₁ and y′₂₂, - - - , y′_(2k) are determinedsimilarly to the design state N₀. These are listed in Table 5. TABLE 5 12 . . . k N₀ y₀₁ y₀₂ . . . y_(0k) N₁ y′₁₁ y′₁₂ . . . y′_(1k) N₂ y′₂₁y′₂₂ . . . y′_(2k)

As to an optical performance here, there are aberrations, Spot RMS andMTF, light intensity, etc. As to conditioning, there are FNO, NA, anobject distance, an image height, etc.

Now, after such data table has been made, the following parameters arecalculated.L1=Σ y ₀ _(j) y′ _(1j) =y ₀₁y′₁₁ +y ₀₂ y′ ₁₂ + . . . +y _(0k) y′ _(1k)L2=Σ y _(0j) y′ _(2j) =y ₀₁ y′ ₂₁ +y ₀₂ y′ ₂₂ + . . . +y _(0k) y′ _(2k)r=Σ y _(0j) ² =y ₀₁ ² +y ₀₂ ² + . . . +y _(0k) ²S _(T) =Σ Σ y′ _(ij) ² =y′ ₁₁ ² +y′ ₁₂ ² + . . . +y′ _(1k) ² +y′ ₂₁ ²+y′ ₂₂ ² + . . . +y′ _(2k) ²S _(β)=(L1+L2)²/2rS _(N×β)=(L1² +L2²)/r−S _(β)S _(e) =S _(T) −S _(β) −S _(N×β)f _(e)=2k−2f _(N)=2k−1V _(e) =S _(e) /f _(e)V _(N)=(S _(N×β) +S _(e))/f _(N)

From the parameters mentioned above, a production error sensitivityparameter X is calculated as follows.X=10 log{(S _(β) −V _(e))/V _(N)}

Seventh Embodiment

A seventh embodiment of a design method of an optical system is shown.Here also, another example in the case of determining for a productionerror sensitivity parameter is shown.

In this embodiment, an example for obtaining a production errorsensitivity parameter when a design state N₀ and a production state N₁exist will be explained. First, as to a design state N₀, opticalperformances y₀₁, y₀₂ - - - , y_(0k) in conditions of 1, 2, - - - , k,are determined. Next, also as to production states N₁, opticalperformances y′₁₁ and y′₁₂, - - - , y′_(1k), are determined similarly tothe design state N₀. An error of A+δ is given in the production stateN₁. Here, since an amount of error is minute, a performance of theproduction state N₂ when an error of A−δ is given can be presumed. Thus,as to a production state N₂, an optical performance y″₂₁ and y″₂₂, - - -, y″_(2k) can be determined as y″_(2j)=2y₀₂−y′_(1j). These are listed inTable 6. TABLE 6 1 2 . . . k N₀ y₀₁ y₀₂ . . . y_(0k) N₁ y′₁₁ y′₁₂ . . .y′_(1k) N₂ y″₂₁ y″₂₂ . . . y″_(2k)

As an optical performance here, there are aberrations, spot RMS, MTF,light intensity, etc. and in conditioning, there are FNO, NA, an objectdistance, an image height, etc.

Now, after such data table have been made, the following parameters arecalculated.L1=Σ y ₀ _(j) y′ _(1j) =y ₀₁ y′ ₁₁ +y ₀₂ y′ ₁₂ + . . . +y _(0k) y′ _(1k)L2=Σ y _(0j) Y″ _(2j) =y ₀₁ y″ ₂₁ +y ₀₂ y″ ₂₂ + . . . +y _(0k) y″ _(2k)r=Σ y _(0j) ² =y ₀₁ ² +y ₀₂ ² + . . . +y _(0k) ²S _(T) =Σ Σ y _(ij) ² =y′ ₁₁ ² +y′ ₁₂ ² + . . . +y′ _(1k) ² +y″ ₂₁ ² +y″₂₂ ² + . . . +y″ _(2k) ²S _(β)=(L1+L2)²/2rS _(N×β)=(L1² +L2²)/r−S _(β)S _(e) =S _(T) −S _(β) −S _(N×β)f _(e)=2k−2f _(N)=2k−1V _(e) =S _(e) /f _(e)V _(N)=(S _(N×β) +S _(e))/f _(N)

From the parameters mentioned above, a production error sensitivityparameter X is as follows.X=10 log{(S _(β) −V _(e))/V _(N)}

FIG. 5 is a diagram showing a constitution of a processing apparatus forcarrying out a method of the present invention. It consists of an inputsection 1 which inputs information required for this design method, anoperation section 2 which carries out an operation required for thedesign method of the present invention, a memory section 3 whichmemorizes a result processed by this operation section 2, and an outputsection 4 which outputs an operation result in a form which can beunderstood by a designer

Information inputted from the input section 1 is once transmitted to theoperation section 3, and a classification and a value of information arejudged, and the information is stored at the memory section 3 if needed.In the memory section 3, contents of the memory section 3 are stored ina specific domain of the memory section 3 by instruction of theoperation section 2. In the operation section 2, according to therunning stage of this method, required information is called from thememory section 3 and operation is carried out and the execution resultis stored in the memory section 3. Finally, as a result of applicationof this method, obtained information is called from the memory section3, and it is transmitted to the output section after having processedinto a state which can be understood by a designer at the operationsection 2. In the output section 4, an output is shown to the designer,based on the information transmitted from the operation section 3.

Next, an example where a method of the present invention is actuallyimplemented by this constitution will be explained by using the firstembodiment. First, as a preparation for start of a flow in the firstembodiment, a various kind of information, such as an amount of errorthat is unchanged during implementation of this method, is inputted fromthe input part 1, and the information is stored in an exclusive storagedomain for keeping a various kind of information in the memory section3.

At step 2, the optical parameter and an amount of error DB of a designstate are called to the operation section 2. In the operation part 2,while referring to information of the amount of error DB to each ofoptical parameters, an optical parameter in a production state is made,otherwise, an optical parameter in an existing production state isrenewed.

At step 3, a parameter of an evaluation function and its assigned weightare inputted from the input part 1, and an evaluation function is made,based on a parameter of the evaluation function inputted by theoperation section 2 and the assigned weight. The valuation function madeby the operation section 2 is stored in the valuation function storagedomain of the memory section 3.

At step 4, the optical parameter of a design state, the opticalparameter of a production state in the memory section 3, and anevaluation function are called to the operation section 2, and then anoperation of optimization is carried out, based on the evaluationfunction called in the operation section 2. The optical parameter of adesign state and the optical parameter of a production state obtainedare stored in each domain of a memory section 3, and information isrenewed.

At step 5, the optical parameter of a design state, the opticalparameter of a production state in the memory section 3, and anevaluation function are called to the operation section 2, and theninformation from the optical parameter of a design state or the opticalparameter of a production state are processed so that it may become aninformation output form defined beforehand, and then these aretransmitted to an output section 4. In the output section 4, theinformation is shown to a designer, based on the processed information.

The designer judges whether these have become a desired specificationand performance, based on the information shown by the output section 4.A design will be completed if it becomes within a range of thespecification and the performance for which the designer requires. If itis not within the range of the desired specification and theperformance, it returns to Step 2 or Step 3, and the procedure mentionedabove is repeated again.

1. A design method of an optical system using an evaluation functioncomprising a step for setting an initial value which sets up an opticalparameter in a design state where a production error has not been takeninto consideration, a step for making/renewing, where an opticalparameter in a production is made by adding the production error to theoptical parameter in the design state, or the production error of theoptical parameter in an existing production state is renewed, a step formaking the evaluation function which makes the evaluation function, anda step for performing optimization which determines an optimal opticalparameter by optimizing the evaluation function.
 2. The design method ofan optical system according to claim 1, wherein in the step for makingfor the production state•renewing, a quantity of the production error tobe applied is acquired, based on a value in a table of an amount oferror which has been established beforehand according to a requirementfor acquisition of an amount of a production error, the amount of theerror is applied to an optical parameter in the design state, and thusan optical parameter in the production state is newly made, or a valueof the amount of error which has been applied to the optical parameterin the existing production state is renewed according to change of theoptical parameter in the design state.
 3. The design method of anoptical system according to claim 1, wherein in the step for making anevaluation function, at least one production error sensitivity parameterdetermined, based on the optical performance of the design state and theproduction state is included as an evaluation parameter, in addition tothe evaluation parameter of the evaluation function.
 4. A design methodof an optical system comprising a step for setting an initial valuewhich sets up a value in a design state as a value of an opticalparameter, a step for setting a production state which sets up a valuein the production state as a value of an optical parameter a step formaking an evaluation function which makes an evaluation function inwhich a production state is a variable, and a step for performingoptimization which optimizes the evaluation function, wherein a value inthe production state is set up by adding a predetermined amount of errorto the value in the design state.
 5. The design method of an opticalsystem according to claim 4, wherein an amount of error is determined,based on a value of a table of an amount of error.
 6. The design methodof an optical system according to claim 5, wherein a value of the tableof an amount of error is determined, based on an actual productionfunction.
 7. The design method of an optical system according to claim5, wherein a table of an amount of error is composed by combination of akind of production error and a kind of optical parameter.
 8. The designmethod of an optical system according to claim 5, wherein the kind ofproduction error contains at least one of Newton error, astigmatism, awall thickness error, a tilt eccentricity, and a shift eccentricity. 9.The design method of an optical system according to claim 5, wherein thekind of optical parameter contains at least one of a radius ofcurvature, a lens thickness, and a lens interval.
 10. The design methodof an optical system according to claim 5, wherein a range in which anoptical parameter can be taken in the error table is divided into two ormore numerical value ranges.
 11. The design method of an optical systemaccording to claim 10, wherein an amount of error is set up to each oftwo or more numerical value ranges.
 12. The design method of an opticalsystem according to claim 4, wherein a step for renewing a productionstate further provided, and the step for renewing a production state isrenewed to a new production error with change of the value of theoptical parameter in a design state, based on the table of an amount oferror.
 13. A processing apparatus comprising an operation section forperforming the design method of an optical system according to claim 1,an input section which inputs information required for the operation, anoutput section which outputs an operation result, and a memory sectionwhich memorizes an operation result.